Three girls, Yoko, Jane and Opal had a total of 2460 marbles. Some exchanges were made. First, Yoko gave Jane as many marbles as Jane had. After that, Jane gave
13 of whatever she had then to Opal. Finally, Opal gave
13 of whatever she had to Yoko. As a result, they each had the same number of marbles. How many marbles did Yoko have at first?
|
Yoko |
Jane |
Opal |
Total |
Before 1 |
? |
1 u |
|
2460 |
Change 1 |
- 1 u |
+ 1 u |
|
|
After 1 |
|
2 u |
|
|
Before 2 |
|
3 p |
|
2460 |
Change 2 |
|
- 1 p |
+ 1 p |
|
After 2 |
|
2 p |
|
|
Before 3 |
|
|
3 boxes |
2460 |
Change 3 |
+ 1 box |
|
- 1 box |
|
After 3 |
|
|
2 boxes |
|
After 3 |
1 group |
1 group |
1 group |
2460 |
3 groups = 2460
1 group = 2460 ÷ 3 = 820
1 group = 2 boxes 2 boxes = 820
1 box = 820 ÷ 2 = 410
2 p = 1 group
1 p = 820 ÷ 2 = 410
3 p = 3 x 410 = 1230
3 p = 2 u
2 u = 1230
1 u = 1230 ÷ 2 = 615
Number of marbles that Yoko had at first
= 1 group - 1 box + 1 u
= 820 - 410 + 615
= 1025
Answer(s): 1025